IAI Actuarial Core Principles · Actuarial Statistics · Linear regression models
In a simple linear regression fitted to n = 12 observations, the estimated slope is 2.50 with standard error 0.80. Using the t-distribution with 10 degrees of freedom (t 0.975 = 2.228), what is the 95% confidence interval for the true slope?
The 95% interval is (0.72, 4.28). It equals the estimate 2.50 plus or minus t(10) of 2.228 times the standard error 0.80, a margin of about 1.78. The t critical value is needed because the error variance is estimated from the data.
- A(0.72, 4.28)Correct
- B(0.92, 4.08)
- C(1.34, 3.66)
- D(0.70, 4.30)
- (-0.78, 5.78)
Explanation
Margin = 2.228 x 0.80 = 1.7824. Interval = 2.50 ± 1.7824 = (0.7176, 4.2824), i.e. (0.72, 4.28). Using 1.96 instead of 2.228 gives (0.93, 4.07), which is wrong because the variance is estimated and the t-distribution is required.
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